Frequency scaling and localization of geodesic acoustic modes in ASDEX Upgrade

The frequency behaviour and localization of the geodesic acoustic mode (GAM), believed to be a coherent plasma turbulence-generated E-r x B zonal flow(ZF) oscillation, is studied in the ASDEX Upgrade tokamak using Doppler reflectometry. In typical elongated (1.4 < kappa < 1.75) plasmas with an X-point divertor configuration the GAM is observed only in the edge density gradient region 0.95 < rho(pol) < 1.0 between the density pedestal top and the flux surface boundary. The GAM frequency (5-25 kHz) is found to scale linearly as omega = Gc(s)/ R-o (sound speed over major radius) but with an inverse dependence on the plasma elongation. and a weak direct dependence on the safety factor q. The lower the GAM frequency the more important it is expected to become in moderating the turbulence via shear decorrelation. A heuristic scaling law for the frequency scale factor G similar to O( 1) involving kappa and finite aspect ratio epsilon terms has been obtained from dedicated parameter scans. For circular plasmas kappa similar to 1 touching the limiter the density pedestal is weakened and the GAM is seen to reach in radially as far as rho(pol) similar to 0.75, depending on the q profile, with a frequency scale G -> root 2 consistent with theoretical predictions. Radially the GAM frequency is not a smooth function but displays a series of plateaus a few centimetres wide coinciding with peaks in the GAM amplitude, suggesting several ZF layers. At the plateau edges the GAM spectral peak splits into two frequency branches.